【leetcode】Longest Valid Parentheses

Longest Valid Parentheses

Given a string containing just the characters '(' and ')', find the length of the longest valid (well-formed) parentheses substring.

For "(()", the longest valid parentheses substring is "()", which has length = 2.

Another example is ")()())", where the longest valid parentheses substring is "()()", which has length = 4.

 

设dp[i]表示从s[i]开始（包括s[i]），到达s[n-1]时，最长的有效括号对的长度。

 

如果s[i]=='('

我们需要检查j=dp[i+1]+i+1对应的s[j]位置的括号是否为")"，如果s[j]为')'则说明又组成了一对括号

故此时dp[i]=dp[i+1]+2

于此同时，我们还需要继续考虑dp[j+1]的值，如果j+1没有超出范围，则dp[i]=dp[i+1]+2+dp[j+1]

 

其他情况dp[i]=0;

 

class Solution {
public:
    int longestValidParentheses(string s) {
        int n=s.length();
        if(n==0) return 0;
       
        int *dp=new int[n];
        dp[n-1]=0;
       
        int result=0;
        for(int i=n-2;i>=0;i--)
        {
            if(s[i]=='(')
            {
                int j=dp[i+1]+i+1;
               
                if(s[j]==')')
                {
                    dp[i]=dp[i+1]+2;
                    if(j<n-1) dp[i]+=dp[j+1];
                }
                else
                {
                    dp[i]=0;
                }
               
                if(dp[i]>result)
                {
                    result=dp[i];
                }
            }
            else
            {
                dp[i]=0;
            }
        }
        delete [] dp;
        return result;
    }
};